Zero-current Nonequilibrium State in Symmetric Exclusion Process with Dichotomous Stochastic Resetting

Abstract

We study the dynamics of symmetric exclusion process (SEP) in the presence of stochastic resetting to two possible specific configurations -- with rate $r_1$ (respectively, $r_2$) the system is reset to a step-like configuration where all the particles are clustered in the left (respectively, right) half of the system. We show that this dichotomous resetting leads to a range of rich behaviour, both dynamical and in the stationary state. We calculate the exact stationary profile in the presence of this dichotomous resetting and show that the diffusive current grows linearly in time, but unlike the resetting to a single configuration, the current can have negative average value in this case. For $r_1=r_2,$ the average current vanishes, and density profile becomes flat in the stationary state, similar to the equilibrium SEP. However, the system remains far from equilibrium and we characterize the nonequilibrium signatures of this `zero-current state'. We show that both the spatial and temporal density correlations in this zero-current state are radically different than in equilibrium SEP. We also study the behaviour of this zero-current state under an external perturbation and demonstrate that its response differs drastically from that of equilibrium SEP -- while a small driving field generates a current which grows as $\sqrt{t}$ in the absence of resetting, the zero-current state in the presence of dichotomous resetting shows a current $\sim t$ under the same perturbation.

arXiv comment29 pages, 12 figures

References in corpus (28)

• Diffusion with Stochastic Resetting
• Stochastic Resetting and Applications
• Diffusion with Optimal Resetting
• Fluctuations and response of nonequilibrium states
• Diffusion in a potential landscape with stochastic resetting
• Diffusion with stochastic resetting at power-law times
• Random walks with preferential relocations to places visited in the past and their application to biology
• Non-equilibrium steady states of stochastic processes with intermittent resetting
• Fluctuating interfaces subject to stochastic resetting
• First passage under stochastic resetting in an interval
• An update on nonequilibrium linear response
• Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics
• Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries
• Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
• Effects of refractory period on stochastic resetting
• Scaled Brownian motion with renewal resetting
• First passage of a particle in a potential under stochastic resetting: a vanishing transition of optimal resetting rate
• Statistical mechanics of the coagulation-diffusion process with a stochastic reset
• Random walk with random resetting to the maximum
• Symmetric Exclusion Process under Stochastic Resetting
• Effect of Partial Absorption on Diffusion with Resetting
• Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
• Transport properties and first arrival statistics of random searches with stochastic reset times
• Stochastic resetting in underdamped Brownian motion
• Spectral content of fractional Brownian motion with stochastic reset
• Stochastic processes subject to a reset-and-residence mechanism: transport properties and first arrival statistics
• Diffusion with Resetting Inside a Circle
• Anomalous diffusion in random-walks with memory-induced relocations

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• Stochastic resetting with stochastic returns using external trap
• Stochastic resetting in interacting particle systems: A review
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• Control of spatiotemporal chaos by stochastic resetting
• Symmetric Exclusion Process under Stochastic Power-law Resetting
• Localization of information driven by stochastic resetting
• Ising Model with Power Law Resetting
• Run-and-tumble particles on a line with a fertile site
• Exact fluctuation and long-range correlations in a single-file model under resetting